Question

look at the math equation. then, choose the best answer.
equation: 456.2 km × 24.6 km =?

1. choose the best answer.

how many significant figures does 24.6 km have?
2
1
4
3

1. choose the best answer.

what is the correct answer using significant figures?
11 222.52 km²
11 200 km²
11 220 km²
11 223 km²

Explanation:

Step1: Count significant figures

Non - zero digits are significant. In \(24.6\), \(2\), \(4\), and \(6\) are non - zero. So, \(24.6\) has \(3\) significant figures.

Step2: Calculate the product

\(456.2\times24.6 = 456.2\times(24 + 0.6)=456.2\times24+456.2\times0.6=(450\times24 + 6.2\times24)+(450\times0.6+6.2\times0.6)=(10800+148.8)+(270 + 3.72)=10948.8+273.72 = 11222.52\)

Step3: Apply significant figure rule

For multiplication, the result should have the same number of significant figures as the factor with the least number of significant figures. \(456.2\) has \(4\) significant figures and \(24.6\) has \(3\). So, we round \(11222.52\) to \(3\) significant figures. \(11222.52\approx11200\) (in scientific notation \(1.12\times10^{4}\) which also has \(3\) significant figures)

Answer:

1. \(3\)
2. \(11200\ km^{2}\)